Numerical Integration and Differentiation

UNIT-III

Numerical Integration and Differentiation

Session-I

Differentiation using Interpolation

Session Objectives

At the end of this session, the learner will be able to:

Write the forward derivative interpolation formulae.
Write the backward derivative interpolation formulae.
Find the intermediate value by forward & backward derivative interpolation formulae.

Teaching Learning Material

Blackboard and chalk

Session Plan

Time
(in min) / Content / Learning Aid & Methodology / Faculty Approach / Learner Activity / Learning Outcomes
05 / Introduces / Chalk and talk / Facilitates / Listens / Remembering
Intrapersonal
05 / Working rule –
Forward
Backward derivative interpolation / Chalk and talk
Question &Answer / Explain / Listens
Writes / Application
Intrapersonal
Linguistic
15 / Solving problems on Forward derivative interpolation / Chalk and talk
Question &Answer / Explain / Listens
Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
15 / Solving problems on
Backward derivative interpolation / Chalk and talk
Question &Answer / Monitors
Instructs
Guides / Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
05 / Conclusion / Summarization / Facilitates / Discusses
Recall
Summarizes / Remembering
Intrapersonal

Session-II

Trapezoidal rule

Session Objectives

At the end of this session, the learner will be able to:

Write the formulae for Trapezoidal rule.
Write the condition for Trapezoidal rule.
Evaluate theintegral by Trapezoidal rule.

Teaching Learning Material

Blackboard and chalk

Session Plan

Time
(in min) / Content / Learning Aid & Methodology / Faculty Approach / Learner Activity / Learning Outcomes
05 / Introduce-
Integration / Chalk and talk / Facilitates / Listens / Remembering
Intrapersonal
05 / Working rule –
Trapezoidal rule / Chalk and talk
Question &Answer / Explain / Listens
Writes / Application
Intrapersonal
Linguistic
15 / Solving problems on Trapezoidal rule / Chalk and talk
Question &Answer / Explain / Listens
Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
15 / Solving problems on Trapezoidal rule / Chalk and talk
Question &Answer / Monitors
Instructs
Guides / Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
05 / Conclusion / Summarization / Facilitates / Discusses
Recall
Summarizes / Remembering
Intrapersonal

Session-III

Simpson’s one third rule

Session Objectives

At the end of this session, the learner will be able to:

Write the formulae for Simpson’s one third rule.
Write the condition for Simpson’s one third rule.
Evaluate the integral bySimpson’s one third rule.

Teaching Learning Material

Blackboard and chalk

Session Plan

Time
(in min) / Content / Learning Aid & Methodology / Faculty Approach / Learner Activity / Learning Outcomes
05 / Recall-
Trapezoidal rule / Chalk and talk / Facilitates / Listens / Remembering
Intrapersonal
05 / Working rule –
Simpson’s one third rule / Chalk and talk
Question &Answer / Explain / Listens
Writes / Application
Intrapersonal
Linguistic
15 / Solving problems on Simpson’s one third rule / Chalk and talk
Question &Answer / Explain / Listens
Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
15 / Solving problems on Simpson’s one third rule / Chalk and talk
Question &Answer / Monitors
Instructs
Guides / Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
05 / Conclusion / Summarization / Facilitates / Discusses
Recall
Summarizes / Remembering
Intrapersonal

Session-IV

Simpson’s 3/8 rule

Session Objectives

At the end of this session, the learner will be able to:

Write the formulae for Simpson’s 3/8 rule.
Write the condition for Simpson’s 3/8 rule.
Evaluate the integral by Simpson’s 3/8 rule.

Teaching Learning Material

Blackboard and chalk

Session Plan

Time
(in min) / Content / Learning Aid & Methodology / Faculty Approach / Learner Activity / Learning Outcomes
05 / Recall-
Simpson’s rule / Chalk and talk / Facilitates / Listens / Remembering
Intrapersonal
05 / Working rule –
Simpson’s 3/8 rule / Chalk and talk
Question &Answer / Explain / Listens
Writes / Application
Intrapersonal
Linguistic
15 / Solving problems on
Simpson’s 3/8 rule / Chalk and talk
Question &Answer / Explain / Listens
Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
15 / Solving problems on
Simpson’s 3/8 rule / Chalk and talk
Question &Answer / Monitors
Instructs
Guides / Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
05 / Conclusion / Summarization / Facilitates / Discusses
Recall
Summarizes / Remembering
Intrapersonal

Session-V

Romberg’s method

Session Objectives

At the end of this session, the learner will be able to:

Write the formulae for Trapezoidal rule.
Write the formulae for Romberg’s method.
Evaluate the integral by Romberg’s method.

Teaching Learning Material

Blackboard and chalk

Session Plan

Time
(in min) / Content / Learning Aid & Methodology / Faculty Approach / Learner Activity / Learning Outcomes
05 / Recall-
Trapezoidal rule / Chalk and talk / Facilitates / Listens / Remembering
Intrapersonal
05 / Working rule –
Romberg’s method / Chalk and talk
Question &Answer / Explain / Listens
Writes / Application
Intrapersonal
Linguistic
15 / Solving problems on
Romberg’s method / Chalk and talk
Question &Answer / Explain / Listens
Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
15 / Solving problems on
Romberg’s method / Chalk and talk
Question &Answer / Monitors
Instructs
Guides / Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
05 / Conclusion / Summarization / Facilitates / Discusses
Recall
Summarizes / Remembering
Intrapersonal

Session-VI

Two point Gaussian Quadrature

Session Objectives

At the end of this session, the learner will be able to:

Write the formulae for two point Gaussian quadrature formulae..
Evaluate the integral by two point Gaussian quadature formulae.

Teaching Learning Material

Blackboard and chalk

Session Plan

Time
(in min) / Content / Learning Aid & Methodology / Faculty Approach / Learner Activity / Learning Outcomes
05 / Introduce-
Two point
Gaussian quadrature / Question &Answer / Facilitates / Participates Recalls
answers / Remembering
Intrapersonal
05 / Working rule –
Two point
Gaussian quadrature / Chalk and talk
Question &Answer / Explain / Listens
Writes / Application
Intrapersonal
Linguistic
15 / Solving problems on
Two point
Gaussian quadrature / Chalk and talk
Question &Answer / Explain / Listens
Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
15 / Solving problems on
Two point
Gaussian quadrature / Chalk and talk
Question &Answer / Monitors
Instructs
Guides / Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
05 / Conclusion / Summarization / Facilitates / Discusses
Recall
Summarizes / Remembering
Intrapersonal

Session-VII

Three point Gaussian Quadrature

Session Objectives

At the end of this session, the learner will be able to:

Write the formulae for three point Gaussian quadrature formulae..
Evaluate the integral by three pointGaussian quadature formulae.

Teaching Learning Material

Blackboard and chalk

Session Plan

Time
(in min) / Content / Learning Aid & Methodology / Faculty Approach / Learner Activity / Learning Outcomes
05 / Recall-
Two point
Gaussian quadrature / Question &Answer / Facilitates / Participates Recalls
answers / Remembering
Intrapersonal
05 / Working rule –
Three point
Gaussian quadrature / Chalk and talk
Question &Answer / Explain / Listens
Writes / Application
Intrapersonal
Linguistic
15 / Solving problems on
Three point
Gaussian quadrature / Chalk and talk
Question &Answer / Explain / Listens
Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
15 / Solving problems on
Three point
Gaussian quadrature / Chalk and talk
Question &Answer / Monitors
Instructs
Guides / Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
05 / Conclusion / Summarization / Facilitates / Discusses
Recall
Summarizes / Remembering
Intrapersonal

Session-VIII

Double Integration using Trapezoidal rule

Session Objectives

At the end of this session, the learner will be able to:

Write the formulae for Trapezoidal rule for double integration.
Evaluate the integral byTrapezoidal rule for double integration

Teaching Learning Material

Blackboard and chalk

Session Plan

Time
(in min) / Content / Learning Aid & Methodology / Faculty Approach / Learner Activity / Learning Outcomes
05 / Introduce-Double integrationby trapezoidal rule / Question &Answer / Facilitates / Participates Recalls
answers / Remembering
Intrapersonal
05 / Working rule –
Trapezoidal rule for double integration / Chalk and talk
Question &Answer / Explain / Listens
Writes / Application
Intrapersonal
Linguistic
15 / Solving problems on
Trapezoidal rule for double integration / Chalk and talk
Question &Answer / Explain / Listens
Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
15 / Solving problems on
Trapezoidal rule for double integration / Chalk and talk
Question &Answer / Monitors
Instructs
Guides / Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
05 / Conclusion / Summarization / Facilitates / Discusses
Recall
Summarizes / Remembering
Intrapersonal

Session-IX

Double Integration using Simpson’s rule

Session Objectives

At the end of this session, the learner will be able to:

Write the formulae for Simpson’s rule for double integration.
Evaluate the integral bySimpson’s rule for double integration

Teaching Learning Material

Blackboard and chalk

Session Plan

Time
(in min) / Content / Learning Aid & Methodology / Faculty Approach / Learner Activity / Learning Outcomes
05 / Recall-Trapezoidal rule for double integration / Question &Answer / Facilitates / Participates Recalls
answers / Remembering
Intrapersonal
05 / Working rule –
Simpson’s rule for double integration / Chalk and talk
Question &Answer / Explain / Listens
Writes / Application
Intrapersonal
Linguistic
15 / Solving problems on
Simpson’s rule for double integration / Chalk and talk
Question &Answer / Explain / Listens
Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
15 / Solvingproblems on
Simpson’s rule for double integration / Chalk and talk
Question &Answer / Monitors
Instructs
Guides / Writes
Discuss / Understanding
Intrapersonal
Mathematical
Logical
05 / Conclusion / Summarization / Facilitates / Discusses
Recall
Summarizes / Remembering
Intrapersonal

Session-X

Tutorial

Session Objectives

At the end of this session, the learner will be able to:

Find the intermediate value by Newton’s forward & backward derivative formulae.
Evaluate the integral by Trapezoidal and Simpson’s rule.

Teaching Learning Material

Blackboard and chalk

Session Plan

me
(in min) / Content / Learning Aid & Methodology / Faculty Approach / Learner Activity / Learning Outcomes
25 / SolvingProblems on Newton’s forward backward derivative / Group Discussion
Q & A / Monitors
Instructs
Guides / Writes
Discuss / Remembering
Intrapersonal
20 / SolveProblems on Trapezoidal , Simpson’s rule / Group Discussion
Q & A / Monitors
Instructs
Guides / Writes
Discuss / Remembering
Intrapersonal

Session-XI

Tutorial

Session Objectives

At the end of this session, the learner will be able to:

Evaluate the integral by Romberg’s method.
Evaluate the integral by Gaussian two point formulae
Evaluate the integral by Gaussian three point formulae

Teaching Learning Material

Blackboard and chalk

Session Plan

Time
(in min) / Content / Learning Aid & Methodology / Faculty Approach / Learner Activity / Learning Outcomes
15 / Solve Problems on Romberg’s method / Group Discussion
Q & A / Monitors
Instructs
Guides / Writes
Discuss / Remembering
Intrapersonal
15 / SolvingProblems on Gaussian two point formulae / Group Discussion
Q & A / Monitors
Instructs
Guides / Writes
Discuss / Remembering
Intrapersonal
15 / SolvingProblems on Gaussian three point formulae / Group Discussion
Q & A / Monitors
Instructs
Guides / Writes
Discuss / Remembering
Intrapersonal

Session-XII

Tutorial

Session Objectives

At the end of this session, the learner will be able to:

Evaluate the double integration using Trapezoidal rule.
Evaluate the double integration using Simpson’s rule.

Teaching Learning Material

Blackboard and chalk

Session Plan

Time
(in min) / Content / Learning Aid & Methodology / Faculty Approach / Learner Activity / Learning Outcomes
20 / Solving problems on Double integration using trapezoidal rule / Group Discussion
Q & A / Monitors
Instructs
Guides / Writes
Discuss / Remembering
Intrapersonal
25 / Solving problems on Double integration using Simpsons rule / Group Discussion
Q & A / Monitors
Instructs
Guides / Writes
Discuss / Remembering
Intrapersonal

Staff-In charge Mission10x- coordinator Principal